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You can put this solution on YOUR website!
\n" ); document.write( "(1) Factor numerator and denominator as needed to get all linear factors:
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\n" ); document.write( "(2) The x-intercept(s) are where g(x) is 0; g(x) is 0 when the numerator is 0. In your example, there is one x-intercept, at x=2. The only x-intercept is (2,0).
\n" ); document.write( "(3) The y-intercept is when x=0; evaluating g(0) gives y = 2/3. The y-intercept is (0,2/3).
\n" ); document.write( "(4) The vertical asymptote(s) are where the denominator is 0. In your example, that is at x=-1 and x=3.
\n" ); document.write( "(5) For large positive or negative values of x, denominator is much larger than the numerator, so the function value has a horizontal asymptote of y=0. Plugging in values shows that the function value is small positive for large positive values of x and small negative for \"large negative\" values of x.
\n" ); document.write( "In summary, we have this:
\n" ); document.write( "(1) function value is small negative for \"large negative\" values of x;
\n" ); document.write( "(2) vertical asymptote at x=-1;
\n" ); document.write( "(3) y-intercept at (0,2/3)'
\n" ); document.write( "(4) the only x-intercept at (2,0);
\n" ); document.write( "(5) vertical asymptote at x=3; and
\n" ); document.write( "(6) function value is small positive for large positive values of x
\n" ); document.write( "You can draw a good representation of the graph with pencil and paper using those constraints.
\n" ); document.write( "It should look like this graph, which is produced by software:
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